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3 years ago

The length of a rectangle is 3 inches more than its width. If the perimeter is 42 inches, find the dimensions of the rectangle.

Mathematics

2 answers:

mojhsa [17]3 years ago

5 0

The problem uses the perimeter formula. P = 2w + 2l where w is the width, and l is the length.

We know the length (l) is 3 inches longer than it's width (or l = w+3). Substitute w +3 into Perimeter equation

P = 2w + 2(w+3). That simplifies to P = 4w + 6.

Since P + 42, we have 42 = 4w +6. With some simple algebra we find that w = 9 and l = 12.

Hope this helps!

eimsori [14]3 years ago

3 0

Width is 12 and length is 9

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Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers

lora16 [44]

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Part A)

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

$\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}$

Where P is the number of eggs laid, x is the number of workers, and y is the daily operating budget (assuming in US dollars $).

We want to find dy/dx.

So, let’s find our equation in terms of x. We can raise both sides to 10/7. Hence:

$\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}$

Simplify:

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Divide both sides by the x term to acquire:

$\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}$

Take the derivative of both sides with respect to x:

$\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]$

Apply power rule. Note that P is simply a constant. Hence:

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Simplify. Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

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We want to evaluate the derivative when x is 30 and when y is $10,000.

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$P=x^{0.3}y^{0.7}$

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$P=(30)^{0.3}(10000)^{0.7}$

Therefore, for our derivative, we will have:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)$

Use a calculator. So:

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Answer:

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Answer:

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